Incorporating holographic dark energy in the big rip cosmological model with \( f(R,\Sigma ,T) - Gravity \)

The primary objective of this research is to investigate the behavior of the universe model in the presence of matter and holographic dark energy in \(f(R,\Sigma ,T) - Gravity\) $f(R,\mathrm{\Sigma },T)-Gravity$ . The study utilizes \(f(R,\,\Sigma ,\,T)\) $f(R,\mathrm{\Sigma },T)$ strong gravity with torsion field equations to derive exact solutions for a Big Rip universe. The research also explores the physical and geometrical aspects of the universe, including the results obtained by Bakry and Shafeek (Indian J Phys 1, 2021). Additionally, the paper introduces a novel cosmological model for Dark energy based on an anti-gravity field scenario. This model may offer a viable solution to the dark energy problem due to the anti-gravity field's existence.